Target Grade Level and Course
7th-9th Grades, Pre-Algebra and Algebra I
Goal
The goal of this performance task is to have students not only be able to calculate the volume of a prism and a cylinder but to also be able to conceptualize the full definition of volume. Specifically, the students will have a meaningful understanding of how to determine volumes even when a formula is not readily available.
Objectives
1. Given two 3D geometric shapes (a prism and a cylinder) students - working in groups - will discuss what dimensions are necessary to determine the volume of the shapes.
2. Students will define the term volume.
3. Given the formula Volume:
Volume = Bh
where,
B = the base area
h = height
students will write out the formula for the volume of a prism and for the volume of a cylinder.
example
Volume Prism = Bh = length x width x height
Volume Cylinder = Bh = πr^2 h
4. Students - working in groups - will discuss how to find the volume of an irregular, solid shape; specifically, will the use of a formula be useful?
5. Students - working in groups - will perform a math-lab in which the volume of an irregularly shaped, solid object's volume will be found using water displacement.
Essential Questions
1. Considering the geometric shapes of the prism and cylinder what dimentions or measurements might be needed to find the volume of each shape?
2. Looking at the formulas a) Volume Prism = LWH and b) Volume Cylinder = πr^2 h can you draw any conclusions about how volume is found for different shapes? Is it easier to see how volume is determined by considering the general formula Volume = Bh , where B = base area and h = height ?
3. How might you find the volume of an unconventional shape such as a solid 3D star?
Lesson
Activity 1 (or situation 1)
1. First, students will break into small groups and use their textbook to define the essential vocabulary words. After, a short discussion will be held where students list household objects that are in the shapes of a prism and/or a cylinder.
Activity 2 (or situation 2)
2. Groups will be given two 3D geometric shapes, one of a rectangular prism and one of a cylinder. Students will discuss how to find the volume of these shapes. For example, which dimension (length, depth, width, height, etc ) would be important? With these shapes students will use the formula Volume = Bh to write out the volume formula for each shape specifically. For example, for the prism instead of writing Volume prism = Bh students will write out Volume prism = length x width x height.
Activity 3 ( or situation 3)
3. Students will perform a lab in which the volume of an irregularly shaped, solid object if determined by water displacement.
Lab Procedure
a) Fill the overflow can with water until the can is completely full.
b) Place the graduated cylinder underneath the nozzle of the overflow can.
c) SLOWLY drop the object into the overflow can.
d) Catch the overflowing water in the graduated cylinder.
e) Once the water has stopped overflowing read the water mark on the graduated cylinder.
f) Record the amount of water in the graduated cylinder (record in your notebook).
Note* The amount of water in the graduated cylinder is the volume of the object because 1cm^3 = 1mL
Reflection Questions
1. We have defined the word volume as the number of cubic units needed to fill a shape. Can you describe what volume is using your own words? Thinking back to the water displacement experiment, can you define volume in terms of the lab?
2. Why does the water displacement method allow us to find the volume of an irregularly shaped, solid object?
3. For our experiment the irregular object was small enough to fit into an overflow container. How would you find the volume of an object too large to fit into our container? What if the object was too large to fit into any container? How would you find the volume then?
Enduring Understandings
1. Being able to visualize and conceptualize an object's volume is an essential real-world skill that can be applied to various situations.
2. Understanding units of measurement can help students problem solve and create solutions that can be read and repeated by mathematicians and scientists.
3. The hands on lab experiment requires students to think critically, work in a group setting, and develop organizational skills.
Materials
1. Geometric Shapes ( one prism and one cylinder for each small group)
2, Textbook or reference material for definitions and formulas
3. Graduated Cylinder (METRIC)
4. Overflow can with a nozzle
5. Water
6. Notebook or paper to record
Standards
1. NCTM Standars 4.2.8 A Geometric Properties
2. NCTM Standards 4,2,8 D Units of Measurement
Grading Rubric for the Math-Lab
A (90-100) - Student has defined all terms, written out the longhand formulas for both the volume of a prism and a cylinder, correctly found the volume of both geometric shapes, written out a complete methodology for the lab experiment, correctly recorded the volume of the object, and exceptionally answered all reflection questions.
B (80-89) - Student has defined all terms, written out the longhand formulas for both the volume of a prism and a cylinder, attempted to find the volume of both geometric shapes (even if incorrect), written out a complete methodology for the lab experiment, recorded the volume of the object the student found even if incorrect, and thoughtfully answered all reflection questions.
C (70-79) - Student has defined at least two terms, written out the longhand formulas for both the volume of a prism and a cylinder, attempted to find the volume of both geometric shapes, written out a methodology for the lab experiment, recorded the volume of the object the student found even if incorrect, and attempted at least two reflection questions.
D (60-69) - Student has defined at least one term, written out the longhand formulas for both the volume of a prism and a cylinder, attempted to find the volume of at least one of the geometric shapes, recorded the volume of the object, and thoughtfully answered at least one reflection questions.
F (below 50) - Student has failed to find the volume of the shapes and has failed to participate in the lab (either by not recording the volume or by not answering the reflection questions)
Topic
Finding the volume of prisms and cylinders
Target Grade Level and Course
7th-9th Grades, Pre-Algebra and Algebra I
Goal
The goal of this performance task is to have students not only be able to calculate the volume of a prism and a cylinder but to also be able to conceptualize the full definition of volume. Specifically, the students will have a meaningful understanding of how to determine volumes even when a formula is not readily available.
Objectives
1. Given two 3D geometric shapes (a prism and a cylinder) students - working in groups - will discuss what dimensions are necessary to determine the volume of the shapes.
2. Students will define the term volume.
3. Given the formula Volume:
Volume = Bh
where,
B = the base area
h = height
students will write out the formula for the volume of a prism and for the volume of a cylinder.
example
Volume Prism = Bh = length x width x height
Volume Cylinder = Bh = πr^2 h
4. Students - working in groups - will discuss how to find the volume of an irregular, solid shape; specifically, will the use of a formula be useful?
5. Students - working in groups - will perform a math-lab in which the volume of an irregularly shaped, solid object's volume will be found using water displacement.
Essential Vocabulary
1, Volume
2. Prism
3. Cylinder
Essential Questions
1. Considering the geometric shapes of the prism and cylinder what dimentions or measurements might be needed to find the volume of each shape?
2. Looking at the formulas a) Volume Prism = LWH and b) Volume Cylinder = πr^2 h can you draw any conclusions about how volume is found for different shapes? Is it easier to see how volume is determined by considering the general formula Volume = Bh , where B = base area and h = height ?
3. How might you find the volume of an unconventional shape such as a solid 3D star?
Lesson
Activity 1 (or situation 1)
1. First, students will break into small groups and use their textbook to define the essential vocabulary words. After, a short discussion will be held where students list household objects that are in the shapes of a prism and/or a cylinder.
Activity 2 (or situation 2)
2. Groups will be given two 3D geometric shapes, one of a rectangular prism and one of a cylinder. Students will discuss how to find the volume of these shapes. For example, which dimension (length, depth, width, height, etc ) would be important? With these shapes students will use the formula Volume = Bh to write out the volume formula for each shape specifically. For example, for the prism instead of writing Volume prism = Bh students will write out Volume prism = length x width x height.
Activity 3 ( or situation 3)
3. Students will perform a lab in which the volume of an irregularly shaped, solid object if determined by water displacement.
Lab Procedure
a) Fill the overflow can with water until the can is completely full.
b) Place the graduated cylinder underneath the nozzle of the overflow can.
c) SLOWLY drop the object into the overflow can.
d) Catch the overflowing water in the graduated cylinder.
e) Once the water has stopped overflowing read the water mark on the graduated cylinder.
f) Record the amount of water in the graduated cylinder (record in your notebook).
Note* The amount of water in the graduated cylinder is the volume of the object because 1cm^3 = 1mL
Reflection Questions
1. We have defined the word volume as the number of cubic units needed to fill a shape. Can you describe what volume is using your own words? Thinking back to the water displacement experiment, can you define volume in terms of the lab?
2. Why does the water displacement method allow us to find the volume of an irregularly shaped, solid object?
3. For our experiment the irregular object was small enough to fit into an overflow container. How would you find the volume of an object too large to fit into our container? What if the object was too large to fit into any container? How would you find the volume then?
Enduring Understandings
1. Being able to visualize and conceptualize an object's volume is an essential real-world skill that can be applied to various situations.
2. Understanding units of measurement can help students problem solve and create solutions that can be read and repeated by mathematicians and scientists.
3. The hands on lab experiment requires students to think critically, work in a group setting, and develop organizational skills.
Materials
1. Geometric Shapes ( one prism and one cylinder for each small group)
2, Textbook or reference material for definitions and formulas
3. Graduated Cylinder (METRIC)
4. Overflow can with a nozzle
5. Water
6. Notebook or paper to record
Standards
1. NCTM Standars 4.2.8 A Geometric Properties
2. NCTM Standards 4,2,8 D Units of Measurement
Grading Rubric for the Math-Lab
A (90-100) - Student has defined all terms, written out the longhand formulas for both the volume of a prism and a cylinder, correctly found the volume of both geometric shapes, written out a complete methodology for the lab experiment, correctly recorded the volume of the object, and exceptionally answered all reflection questions.
B (80-89) - Student has defined all terms, written out the longhand formulas for both the volume of a prism and a cylinder, attempted to find the volume of both geometric shapes (even if incorrect), written out a complete methodology for the lab experiment, recorded the volume of the object the student found even if incorrect, and thoughtfully answered all reflection questions.
C (70-79) - Student has defined at least two terms, written out the longhand formulas for both the volume of a prism and a cylinder, attempted to find the volume of both geometric shapes, written out a methodology for the lab experiment, recorded the volume of the object the student found even if incorrect, and attempted at least two reflection questions.
D (60-69) - Student has defined at least one term, written out the longhand formulas for both the volume of a prism and a cylinder, attempted to find the volume of at least one of the geometric shapes, recorded the volume of the object, and thoughtfully answered at least one reflection questions.
F (below 50) - Student has failed to find the volume of the shapes and has failed to participate in the lab (either by not recording the volume or by not answering the reflection questions)